Contact lines are the locations where a gas, liquid and a solid meet. From everyday experience we know that such contact lines can be mobile, for example in the case of a water droplet sliding over a glass surface. However, the continuum description of the flow towards or away from a contact line implies that the forces diverge as one approaches a moving contact line. This fundamental problem is of relevance to many applications, and in particular to the development and application of immersion lithography, where a liquid droplet is positioned between the lithographic optical head and the substrate that moves under it. This contribution will address experiments dealing with the shape and stability of a moving droplet and experiments that investigate the underlying behaviour of the nanoscale structure of the moving contact line.